Parallel resistor calculator
This parallel resistor calculator gives the total value of resistors in parallel – and likewise in series, for capacitors and for inductors. The resistors 100, 220 and 470 Ω in parallel come to 60 Ω (exactly 59.98 Ω); at 12 V a total of 200 mA flows.
Source: Wikipedia – Series and parallel circuits (resistors, capacitors, inductors). Updated: .
How it is calculated
How to calculate resistors in parallel
In a parallel circuit the reciprocals add up: 1/R = 1/R₁ + 1/R₂ + 1/R₃ + …. For two resistors R = R₁ · R₂ ÷ (R₁ + R₂) is enough, and for n equal resistors R ÷ n. The total is always smaller than the smallest single resistor.
Example
100 Ω, 220 Ω and 470 Ω in parallel: 1/100 + 1/220 + 1/470 = 0.016673 S, so R = 59.98 Ω. At 12 V the branches carry 120 mA, 54.5 mA and 25.5 mA, 200 mA in total, and the power is about 2.4 W.
Series circuits, capacitors and inductors
- Resistors in series: the values add, the current is the same everywhere and the voltage divides.
- Capacitors behave the other way round: in parallel the capacitances add, in series the reciprocals do.
- Inductors follow the same rule as resistors as long as they are not magnetically coupled.
Entering values and standard values
Values may carry a prefix: k, M, G and m, µ, n, p. “4k7” means 4.7 kΩ. Along with the result the calculator names the nearest values of the E12 and E24 series (IEC 60063) that are common in shops; E12 usually goes with 10% and E24 with 5% tolerance.
Honest limits
The calculation uses ideal components. Tolerances, temperature drift, capacitor losses and AC impedance are not included. In real circuits, check the power rating of each resistor.
Frequently asked questions
How do I calculate total resistance in parallel?
Use 1/R = 1/R₁ + 1/R₂ + …. For 100 Ω and 220 Ω that gives 68.75 Ω.
What is the formula for two resistors in parallel?
R = R₁ · R₂ ÷ (R₁ + R₂). Two equal resistors give half of one.
Why is the total smaller than the smallest resistor?
Every extra branch gives the current another path, so conductance rises and resistance falls.
How do I calculate capacitors in parallel or series?
In parallel the capacitances add; in series 1/C = 1/C₁ + 1/C₂ + …. Choose “Capacitors” here.
How do I enter 4.7 kΩ or 100 nF?
As 4.7k, 4k7 or 100n. The calculator understands the prefixes p, n, µ, m, k, M and G.
Sources and legal basis
- Wikipedia – Series and parallel circuits (resistors, capacitors, inductors)
- Wikipedia – E series of preferred numbers (IEC 60063)
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